Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:206AI GHM
Order: 20
Horizontal side: 206 Vertical side: 206
Elements: 6, 18, 14√2, 24, 18√2, 28, 30, 24√2, 36, 28√2, 30√2, 33√2, 56, 47√2, 75, 56√2, 84, 103, 122, 103√2.
Code: 1227 0 206 560 122 206 561 178 206 282 206 178 281 206 206 753 206 103 363 66 114 182 84 132 181 84 150 332 117 117 474 131 103 246 60 108 140 117 117 300 30 114 301 60 114 67 60 114 245 60 84 1030 103 103 1031 206 103 847 0 84
The properties below may precede order:side in a tiling's title:
- c = crossed. There is a tile-corner traversed by two lines. The only known crossed PPIRTS's below order 20 are 19:35AB1of4 and 19:35AB4of4.
- d = double-pentagon patterned. Every such tiling is a subdivision of an instance of the same deformable tiling by two 45-90-90-90-225 pentagons with a shared side, four triangles and two pseudotriangles. All below order 19 are degenerate in the sense that one or more sides of underlying tiles have shrunk to zero length. The non-degenerate d-tilings of order 19 are 19:221AA, 19:229AB and 19:241AA.
- e = elegant. No tile-corner is just a T-junction. Such tilings may be considered aesthetically pleasing. The only known elegant PPIRTS's below order 16 are 13:21AA, 14:26AJ, 14:35AA and 15:55AA.
- i = isomers exist which are ineligible for this catalogue. They are not included in the isomer count which follows 'of' in the tiling id.
- r = rectangular inclusion. The only known PPIRTS's below order 16 with a rectangular inclusion are 13:18AA1-4of4 and 15:44AA1-4of4.
Credit for Discovery
Just three people are credited with the discovery of Primitive Perfects:
Geoffrey H. Morley (GHM, England)
Jasper D. Skinner, II (JDS, United States)
William T. Tutte (WTT, Canada, 1917-2002) (15:44AI, 17:136AJ and 19:56AJ only)